Mathematical Models and Degradation Forecast of Arid Soil–Plant Systems

IF 0.6 Q4 ECOLOGY
A. N. Salugin, K. N. Kulik
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Abstract

Mathematical modeling is considered as a method for studying the dynamics of grassland soil and plant systems in arid zones of Russia. The evolutionary development of grassland phytocenoses was modeled using the principles of nonequilibrium thermodynamics based on continuous and discrete mathematical formalisms. Examples are given, and problems of sustainable development of such systems under conditions of anthropogenic load and climate change are discussed. This study demonstrates new methodological capabilities of mathematical models of different types: in the form of systems of ordinary differential equations and discrete Markov chains. Prediction of degradation processes occurring in grasslands using these models has been studied in a comparative aspect. Differential models with constant and variable coefficients showed different results due to the nonlinearity of succession dynamics. The model with constant coefficients was refined by introducing time-dependent coefficients. The stability of the functioning of grassland ecosystems is discussed from the point of view of the formal parametric stability of solutions for a system of ordinary differential equations. Discrete modeling using the Markov chain technique showed that the degradation of soil and plant systems when the animal load is exceeded is described by a heterogeneous Markov process. Homogeneous Markov chains give adequate forecasts on one observation time interval. Prediction of the final states in the homogeneous approximation revealed that the observed nonlinearity in the dynamics of phytocenoses was caused by changes in the rate of development, ultimately leading to heterogeneity of the Markov chain. The issues of modeling nonlinear processes in the ecology of grassland soil and plant systems in the context of heterogeneous Markov processes are discussed.

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Abstract Image

干旱土壤-植物系统的数学模型和退化预测
摘要 数学建模被认为是研究俄罗斯干旱地区草原土壤和植物系统动态的一种方法。利用基于连续和离散数学形式的非平衡热力学原理,对草地植物群落的进化发展进行了建模。研究举例说明了在人为负荷和气候变化条件下此类系统的可持续发展问题。这项研究展示了不同类型数学模型的新方法能力:常微分方程系统和离散马尔可夫链形式。利用这些模型对草原退化过程的预测进行了比较研究。由于演替动力学的非线性,系数恒定和系数可变的微分模型显示出不同的结果。通过引入随时间变化的系数,对恒定系数模型进行了改进。从常微分方程系统解的形式参数稳定性角度讨论了草原生态系统功能的稳定性。利用马尔可夫链技术进行的离散建模表明,当动物负荷超标时,土壤和植物系统的退化可以用异质马尔可夫过程来描述。同质马尔可夫链可在一个观测时间间隔内进行充分预测。对同质近似的最终状态进行预测后发现,观察到的植物动态非线性是由发展速度的变化引起的,最终导致马尔可夫链的异质性。在异质马尔可夫过程的背景下,讨论了草地土壤和植物系统生态学中的非线性过程建模问题。
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来源期刊
Arid Ecosystems
Arid Ecosystems ECOLOGY-
CiteScore
1.50
自引率
25.00%
发文量
59
期刊介绍: Arid Ecosystems  publishes original scientific research articles on desert and semidesert ecosystems and environment:systematic studies of arid territories: climate changes, water supply of territories, soils as ecological factors of ecosystems state and dynamics in different scales (from local to global);systematic studies of arid ecosystems: composition and structure, diversity, ecology; paleohistory; dynamics under anthropogenic and natural factors impact, including climate changes; studying of bioresources and biodiversity, and development of the mapping methods;arid ecosystems protection: development of the theory and methods of degradation prevention and monitoring; desert ecosystems rehabilitation;problems of desertification: theoretical and practical issues of modern aridization processes under anthropogenic impact and global climate changes.
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